1. Field of the Invention
The present invention relates to an apparatus for and a method of evaluating the polarization characteristic of a ferroelectric capacitor.
2. Description of the Related Art
Developments of nonvolatile ferroelectric memories utilizing the polarization hysteresis characteristic of a ferroelectric capacitor progress energetically. An apparatus and method for evaluating the polarization characteristic of a ferroelectric capacitor formed on a semiconductor substrate are vital to the memory developments. A SAWYER TOWER circuit is generally used in the polarization-characteristic evaluating apparatus at the present stage of this technical field.
A conventional apparatus for evaluating the polarization characteristic of a ferroelectric capacitor is shown in FIG. 29. In the FIG. 29, 1 is a semiconductor substrate; 2 is a ferroelectric capacitor; 2a is a first electrode of the ferroelectric capacitor 2; 2b is a second electrode of the same; 3 and 4 are wires; and 5 and 6 are pads. The ferroelectric capacitor 2, wires 3 and 4, and pads 5 and 6 are formed on and in the semiconductor substrate 1. Numeral 7 is a reference capacitor; 8 is a pulse generator which generates pulse signals of arbitrary waveforms; 9 is an oscilloscope; and 10 to 12 are cables. Numeral 7a is a first electrode of the reference capacitor 7; 7b is a second electrode of the same; 8a is an output terminal of the pulse generator 8; 9a is a first input terminal of the oscilloscope 9; and 9b is a second input terminal of the same. A capacitance value of the reference capacitor 7 is known.
A conventional method for evaluating the polarization characteristic of a ferroelectric capacitor is flow charted in FIG. 30.
Waveform diagrams showing voltage pulses produced by the pulse generator 8 and voltages measured and viewed by the oscilloscope 9 in evaluating the polarization characteristic of the ferroelectric capacitor by the FIG. 29 apparatus are shown in FIG. 31. In FIG. 31, (a) and (d) are the voltage pulses generated by the pulse generator 8; (b) and (e) are the voltages that are applied to the first input terminal 9a of the oscilloscope 9 and measured and observed in their waveforms by the oscilloscope; (c) and (f) are the voltages that are applied to the second input terminal 9b thereof and measured and observed in their waveforms by the oscilloscope. In the graph of FIG. 31, the vertical scale for the waveforms (c) and (f) is shorter than that for the waveforms (a) and (d), and (b) and (e). Further, numerals 51, 52 and 53 represent voltage pulses (whose waveforms are trapezoidal) generated by the pulse generator 8; 54 and 55, the voltages that are applied to the first input terminal 9a of the oscilloscope 9 and measured and viewed in their waveforms by the oscilloscope; and 56 and 57, the voltages that are applied to the second input terminal 9b thereof and measured and viewed in their waveforms by the oscilloscope. Also in FIG. 31, t1 indicates a time point where the voltage 54 starts to vary; and t2, a time point where the voltage 55 starts to vary.
A polarization characteristic of the ferroelectric capacitor, which is measured by the conventional polarization characteristic evaluating apparatus, is as shown in FIG. 32. In the figure, reference numerals 71 and 72 are polarization hysteresis curves of the ferroelectric capacitor; 73 is a polarization quantity of the capacitor at time point t1; and 74 is a polarization quantity of the same at time point t2.
How the prior polarization-characteristic evaluating apparatus evaluates the polarization characteristic of a ferroelectric capacitor will be described with reference to FIGS. 29 to 32.
[Step P1, FIG. 30]
A first trapezoidal (waveform) voltage pulse 51 that is generated by the pulse generator 8 is first applied to the ferroelectric capacitor 2. With the pulse application, a polarization state of the ferroelectric capacitor 2 is set to a first preset state.
[Step P2]
Then, a second trapezoidal voltage pulse 52 that is generated by the pulse generator 8 is applied to and across the ferroelectric capacitor 2. Voltages 54 and 56 that appear at the first and second input terminals 9a and 9b of the oscilloscope 9, are measured and viewed in their waveforms are measured and observed by the oscilloscope.
[Step P3]
The items of task done in this step are:
1) to calculate a variation of the electric field placed across the ferroelectric capacitor 2 with respect to time by using a thickness of the thin film of the ferroelectric capacitor 2 and the voltage 54; PA1 2) to calculate a variation of the amount of the charge at the second electrode 2b of the ferroelectric capacitor 2 with respect to time when the second voltage pulse 52 is applied to the capacitor, by using the capacitance of the reference capacitor 7 and the voltage 56; PA1 3) to obtain a relationship between the electric field applied to the ferroelectric capacitor 2 and the amount of the charge at the second electrode 2b of the ferroelectric capacitor 2; and PA1 4) to depict a first polarization hysteresis curve 71 on the basis of the obtained relationship, with a value midway between the maximum and minimum amounts of the charge being set at a zero point of the polarization quantity of the capacitor. PA1 1) to calculate a variation of the electric field applied to the ferroelectric capacitor 2 with respect to time by using a thickness of the thin film of the ferroelectric capacitor 2 and the waveform of the voltage 55; PA1 2) to calculate a variation of the amount of the charge at the second electrode 2b of the ferroelectric capacitor 2 with respect to time when the second voltage pulse 52 is applied to the capacitor, by using the capacitance of the reference capacitor 7 and the voltage 57; PA1 3) to obtain a relationship between the electric field applied to the ferroelectric capacitor 2 and the amount of the charge at the second electrode 2b of the ferroelectric capacitor 2; and PA1 4) to depict a second polarization hysteresis curve 72 on the basis of the obtained relationship, with a value halfway between the maximum and minimum amounts of the charge being set at a zero point of the polarization quantity of the capacitor.
[Step P4]
A third trapezoidal voltage pulse 53 that is generated by the pulse generator 8 is applied to the ferroelectric capacitor 2. With the pulse application, a polarization state of the ferroelectric capacitor 2 is set to a second predetermined state.
[Step P5]
The second voltage pulse 52 that is generated by the pulse generator 8 is applied to the ferroelectric capacitor 2. Voltages 55 and 57 that appear at the first and second input terminals 9a and 9b of the oscilloscope 9, are measured and viewed in their waveforms by the oscilloscope.
[Step P6]
The items of task done in this step are:
[Step P7]
A difference between the polarization quantities 73 and 74 is calculated to obtain a nonvolatile polarization.
The conventional polarization-characteristic evaluating apparatus and method have the following disadvantages.
In the polarization-characteristic evaluating apparatus or the measuring system shown in FIG. 29, the cable 10 has a parasitic capacitance of several tens pF or larger. It is the ferroelectric capacitor of about 1 nF that can reliably be measured in its polarization characteristic while being free from the influence by the parasitic capacitance.
In analyzing the operations of the nonvolatile ferroelectric memory, a voltage pulse used must be 100 ns or shorter in pulse width. For evaluating a variation of the polarization of the ferroelectric capacitor of the memory by using the FIG. 29 measuring system, if the voltage pulse of such a short pulse width is used, a switching time is long since the parasitic capacitance of the cable is large. The long switching time may produce ringing and deformation of the waveform of the voltage pulse. In the measurement, if the voltage pulse of the deformed waveform is applied to the ferroelectric capacitor, the resultant evaluation of the nonvolatile polarization of the ferroelectric memory will be incorrect. For this reason, the use of a voltage pulse of a short pulse width is rejected by the conventional polarization-characteristic evaluating apparatus.
In the FIG. 29 evaluating apparatus, the capacitance of the reference capacitor 7 varies with frequency. The fact makes it difficult to maintain a constant capacitance over a frequency region of several MHz or higher. Therefore, the evaluation of a polarization variation of the ferroelectric capacitor by using the voltage pulse of 100 ns or shorter in pulse width will provide an unreliable evaluation result. A measurement of a variation of the polarization from a polarization state is inevitably performed in analyzing the operations of the nonvolatile ferroelectric memory. However, such a measurement is impossible when the prior polarization-characteristic evaluating apparatus is used. Meanwhile, a reliability simulation test provides an unreliable test result where the pulse width of an AC voltage pulse is different from that of a pulse applied to the ferroelectric capacitor in the memory. The polarization characteristic of the ferroelectric capacitor of the memory will be deteriorated when it undergoes a repetition of rewriting operations, which is performed by applying AC voltage pulses to the ferroelectric capacitor. To check the deterioration of the polarization characteristic of such ferroelectric capacitor, the ferroelectric capacitor is subjected to a reliability simulation test. In this test, the pulse width of the voltage pulse must be at least 100 ns, and the result is a long testing time. In the simulation test, the arbitrary-waveform pulse generator is used for a long time. The result is an increase of the number of evaluating means and the cost to evaluate.